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Algorithm

We briefly describe the usage of formulae presented here in each step in the algorithm of FM-BIEM with the hypersingular integral equation [the regularised integral equation] (See chapter 2 for more details).
Steps 1-2. Same as the steps 1-2 in the algorithm described in chapter 2.
Step 3. Computation of the multipole moments:

In this step we use (3.53) and (3.54) [(3.83) and (3.84)] for the computation of the multipole moments associated with leaves. Also, we use (3.57) and (3.58) [(3.71) and (3.72)] for M2M translations tracing the tree structure of cells upward (decreasing $l(\ge2)$).

Step 4. Computation of the local expansion: In this step we use (3.60) and (3.61) [(3.74) and (3.75)] for M2L translations and (3.64) and (3.65) [(3.78) and (3.79)] for L2L translations tracing the tree structure of cells downward (increasing $l(\ge2)$).

Step 5. Evaluation of the integral in (3.46): In this step we use (3.80)[(3.80)] for the direct computation and use (3.59) [(3.73)] for the evaluation of contributions with the local expansion.


next up previous contents
Next: Numerical examples Up: Numerical procedures Previous: Analytical computation of the
Ken-ichi Yoshida
2001-07-28